Inter-symbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable. One of the causes of ISI is multipath propagation in which a wireless signal from a transmitter reaches the receiver via many different paths. The causes of this include reflection (i.e., the signal may bounce off buildings), refraction (such as through the foliage of a tree) and atmospheric effects such as atmospheric ducting and ionospheric reflection. Since all of these paths are of different lengths, this results in the different versions of the signal arriving at different times, resulting in ISI.
Data communication schemes have handled ISI by a variety of techniques. One such technique is known as Orthogonal Frequency Division Multiplexing (OFDM). OFDM uses modulation waveforms that enable the essential removal of ISI in a frequency-dependent channel. For example, in OFDM, each transmitted data block is a weighted superposition of OFDM modulation waveforms. The OFDM modulation waveforms form an orthonormal basis set over a time period (TS-TG) where TS is the length of the OFDM block (also referred to as symbol-interval of duration TS) and TG is the duration of either a guard interval or a cyclic prefix, both expressed as a multiple of the sampling interval. Because ISI does not distort symbols separated by more than the communication channel's delay-spread TD, the guard interval TG is selected to be greater than or equal to the delay spread TD in OFDM. In an OFDM block, the weights of the superposition define the data symbol being transmitted.
At the receiver, in OFDM, each transmitted data block is demodulated by projecting the received data block onto a basis set of conjugate OFDM modulation waveforms. Because the OFDM modulation waveforms are a basis set over the period (TS-TG), the projections may be performed over the last period (TS-TG) of the OFDM data blocks. That is, the projections do not need to use prefix portions of the OFDM data blocks. Because the channel memory is limited to a time of length TD, an earlier transmitted OFDM block only produces ISI in the cyclic prefix or guard portion of the next received OFDM data block. Thus, by ignoring said cyclic prefix or guard portions of received OFDM data blocks, OFDM produces demodulated data that is free of distortion due to ISI. OFDM techniques may also effectively diagonalize the communication channel.
Unfortunately, cyclic prefix and guard portions of OFDM data blocks consume bandwidth that might otherwise be used to transmit data. As the communication channel's delay-spread TD approaches the temporal length of the OFDM data block TS, the bandwidth TS-TD remaining for carrying data shrinks to zero. For example, when the channel delay-spread is equal to the symbol interval, then OFDM is 0% efficient because the redundant cyclic prefix occupies the entire symbol interval. Increasing the symbol interval TS would alleviate this problem, but this results in increased communication delay, which might not be tolerable depending on the application.
In order to overcome the bandwidth-deficient channel whose delay-spread approaches the length of the OFDM block, Chen et al. (U.S. Pat. No. 7,653,120) introduces a Channel Adaptive Waveform Modulation (CAWM) that generates modulating waveforms from the channel impulse response itself. When the channel delay-spread is equal to the symbol interval, CAWM is 50% efficient because the number of orthogonal data-symbol-bearing waveforms that can be created is equal to half the symbol-interval. When the delay-spread is equal to twice the symbol interval, then CAWM is ⅓ (33%) efficient. This compares to a 0% efficiency of OFDM in both cases.